Auction-Based Distributed Resource Allocation for Cooperation Transmission in Wireless Networks

Cooperative transmission can greatly improve communication system performance by taking advantage of the broadcast nature of wireless channels. Most previous work on resource allocation for cooperation transmission is based on centralized control. In this paper, we propose two share auction mechanisms, the SNR auction and the power auction, to distributively coordinate the resource allocation among users. We prove the existence, uniqueness and effectiveness of the auction results. In particular, the SNR auction leads to a fair resource allocation among users, and the power auction achieves a solution that is close to the efficient allocation.Comment: To appear in the Proceedings of the IEEE IEEE Global Communications Conference (GLOBECOM), Washington, DC, November 26 - 30, 200

Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

Designing Coalition-Proof Reverse Auctions over Continuous Goods

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the incentive-compatible Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of a polymatroid-type. These conditions, however, do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof without any extra conditions on the submitted bids and the constraint sets. Since calculating the payments directly for these mechanisms is computationally difficult for auctions involving many participants, we present two computationally efficient methods. Our results are verified with several case studies based on electricity market data

A Mechanism for Fair Distribution of Resources without Payments

We design a mechanism for Fair and Efficient Distribution of Resources (FEDoR) in the presence of strategic agents. We consider a multiple-instances, Bayesian setting, where in each round the preference of an agent over the set of resources is a private information. We assume that in each of r rounds n agents are competing for k non-identical indivisible goods, (n > k). In each round the strategic agents declare how much they value receiving any of the goods in the specific round. The agent declaring the highest valuation receives the good with the highest value, the agent with the second highest valuation receives the second highest valued good, etc. Hence we assume a decision function that assigns goods to agents based on their valuations. The novelty of the mechanism is that no payment scheme is required to achieve truthfulness in a setting with rational/strategic agents. The FEDoR mechanism takes advantage of the repeated nature of the framework, and through a statistical test is able to punish the misreporting agents and be fair, truthful, and socially efficient. FEDoR is fair in the sense that, in expectation over the course of the rounds, all agents will receive the same good the same amount of times. FEDoR is an eligible candidate for applications that require fair distribution of resources over time. For example, equal share of bandwidth for nodes through the same point of access. But further on, FEDoR can be applied in less trivial settings like sponsored search, where payment is necessary and can be given in the form of a flat participation fee. To this extent we perform a comparison with traditional mechanisms applied to sponsored search, presenting the advantage of FEDoR

Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension

Algorithmic mechanism design (AMD) studies the delicate interplay between computational efficiency, truthfulness, and optimality. We focus on AMD's paradigmatic problem: combinatorial auctions. We present a new generalization of the VC dimension to multivalued collections of functions, which encompasses the classical VC dimension, Natarajan dimension, and Steele dimension. We present a corresponding generalization of the Sauer-Shelah Lemma and harness this VC machinery to establish inapproximability results for deterministic truthful mechanisms. Our results essentially unify all inapproximability results for deterministic truthful mechanisms for combinatorial auctions to date and establish new separation gaps between truthful and non-truthful algorithms

Pigouvian pricing and stochastic evolutionary implementation

pricing;game theory

Price-Based Combinatorial Auction: Connectedness and Representative Valuations

We investigate combinatorial auctions from a practical perspective. The auctioneer gathers information according to a dynamical protocol termed ask price procedure. We demonstrate a method for elucidating whether a procedure gathers sufficient information for deriving a VCG mechanism. We calculate representative valuation functions in a history-contingent manner, and show that it is necessary and sufficient to examine whether efficient allocations with and without any buyer associated with the profile of representative valuation functions were revealed. This method is tractable, and can be applied to general procedures with connectedness. The representative valuation functions could be the sufficient statistics for privacy preservation.